AC9M9M03Year 9MeasurementPractised on site

AC9M9M03 — Year 9 Measurement

Official Curriculum Content Description:

solve spatial problems, applying angle properties, scale, similarity, Pythagoras’ theorem and trigonometry in right-angled triangles

Worked Examples (2)

Example 1Area & Volume Ratios under Scaling

Solid A has a volume of

30\text{ m}^3

. Solid A is enlarged by a length scale factor of

k = 5

to form Solid B. Calculate the volume of Solid B.

Common mistake: Applying the length scale factor

k

directly to volume instead of

k^3

Correct Answer:

3750\text{ m}^3

Accepted: A unit is optional (m^3, m³, cu m all accepted).

Worked Solution:

1. Volume scale factor =

k^3 = 5^3 = 125

. 2. Volume of Solid B =

30 \times 125 = 3750\text{ m}^3

Example 2Angles of Elevation & Depression

An observer stands

75\text{ m}

away from the base of a vertical tower. The angle of elevation to the top of the tower is

55^\circ

. Calculate the height of the tower

h

. Give your answer to 1 decimal place.

Diagram not accurately drawn

Common mistake: Measuring the angle of elevation from the vertical tower line instead of the horizontal ground line.

Correct Answer:

107.1\text{ m}

Accepted: A unit is optional (m accepted).

Worked Solution:

1. The ground distance, tower height, and line of sight form a right-angled triangle. 2.

\tan(55^\circ) = \frac{\text{height}}{\text{distance}} = \frac{h}{75}

. 3.

h = 75 \times \tan(55^\circ) \approx 107.1\text{ m}

Work through unlimited interactive questions for this curriculum skill, with instant answers and step-by-step methods.